1
JEE Main 2020 (Online) 2nd September Evening Slot
+4
-1
The imaginary part of
$${\left( {3 + 2\sqrt { - 54} } \right)^{{1 \over 2}}} - {\left( {3 - 2\sqrt { - 54} } \right)^{{1 \over 2}}}$$ can be :
A
-2$$\sqrt 6$$
B
6
C
$$\sqrt 6$$
D
-$$\sqrt 6$$
2
JEE Main 2020 (Online) 2nd September Morning Slot
+4
-1
The value of

$${\left( {{{1 + \sin {{2\pi } \over 9} + i\cos {{2\pi } \over 9}} \over {1 + \sin {{2\pi } \over 9} - i\cos {{2\pi } \over 9}}}} \right)^3}$$ is :
A
$${1 \over 2}\left( {\sqrt 3 - i} \right)$$
B
-$${1 \over 2}\left( {\sqrt 3 - i} \right)$$
C
$$- {1 \over 2}\left( {1 - i\sqrt 3 } \right)$$
D
$${1 \over 2}\left( {1 - i\sqrt 3 } \right)$$
3
JEE Main 2020 (Online) 9th January Evening Slot
+4
-1
If z be a complex number satisfying |Re(z)| + |Im(z)| = 4, then |z| cannot be :
A
$$\sqrt {10}$$
B
$$\sqrt {7}$$
C
$$\sqrt {{{17} \over 2}}$$
D
$$\sqrt {8}$$
4
JEE Main 2020 (Online) 9th January Morning Slot
+4
-1
Let z be complex number such that
$$\left| {{{z - i} \over {z + 2i}}} \right| = 1$$ and |z| = $${5 \over 2}$$.
Then the value of |z + 3i| is :
A
$$2\sqrt 3$$
B
$$\sqrt {10}$$
C
$${{15} \over 4}$$
D
$${7 \over 2}$$
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